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High School Math : How to find the slope of a perpendicular line

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

A line passes through the points (2,1) and (5,12) . If a new line is drawn perpendicular to the original line, what will its slope be?

Possible Answers:

$\frac{5}{4}$

$\frac{-3}{11}$

$\frac{-3}{5}$

-4/5

$\frac{3}{11}$

Correct answer:

$\frac{-3}{11}$

Explanation:

The original line has a slope of $\frac{11}{3}$ , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

Which of the following is the equation of a line that is perpendicular to the line y = 3x - 5 ?

Possible Answers:

y = -3x + 4

y = 2x - 5

$y = \frac{1}{3}x + 6$

y = 3x + 10

$y = -\frac{1}{3}x + 10$

Correct answer:

$y = -\frac{1}{3}x + 10$

Explanation:

Perpendicular lines have slopes that are the opposite reciprocals of each other. Thus, we first identify the slope of the given line, which is (since it is in the form y = mx + b , where represents slope).

Then, we know that any line which is perpendicular to this will have a slope of $-\frac{1}{3}$ .

Thus, we can determine that $y = -\frac{1}{3}x + 10$ is the only choice with the correct slope.

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Example Question #2 : How To Find The Slope Of A Perpendicular Line

What will be the slope of the line perpendicular to $y=3x+\frac{1}{2}$ ?

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

In standard y=mx+b form, the is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is . Therefore, the slope of the perpendicular line is $-\frac{1}{3}$ .

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Example Question #4 : How To Find The Slope Of A Perpendicular Line

Which of the following is perpendicular to the line described by

y = 3x+5

Possible Answers:

$y=-\frac{1}{2}x+4$

y=-3x+2

y=-3x+7

$y=-\frac{1}{3}x+2$

$y=\frac{1}{3}x+5$

Correct answer:

$y=-\frac{1}{3}x+2$

Explanation:

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be $-\frac{1}{3}$ .

The answer

$y=-\frac{1}{3}x+2$

is the only equation listed that has a slope of $-\frac{1}{3}$ .

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Example Question #3 : How To Find The Slope Of A Perpendicular Line

Which of the following is perpendicular to the line described by y = -6x+3

Possible Answers:

$y = -\frac{1}{6}x+9$

y = -6x+9

$y = \frac{1}{6}x+9$

y = 6x+9

Correct answer:

$y = \frac{1}{6}x+9$

Explanation:

The answer

$y = \frac{1}{6}x+9$

is the only equation listed that has a slope of $\frac{1}{6}$ .

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Example Question #2 : How To Find The Slope Of A Perpendicular Line

Which of the following gives the slope of a line that is perpendicular to y = -3x + 8 ?

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{3}$

Explanation:

Recall that the slopes of perpendicular lines are opposite reciprocals of one another. As a result, we are looking for the opposite reciprocal of . Thus, we can get that the opposite reciprocal is $\frac{1}{3}$ .

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Example Question #4 : How To Find The Slope Of A Perpendicular Line

Find the slope of the line perpendicular to $y + \frac{2}{3}x = 12$ .

Possible Answers:

$-\frac{2}{3}$

$\frac{3}{2}$

$-\frac{3}{2}$

$-\frac{1}{12}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

Put this equation into slope-intercept form, y = mx + b, to find the slope, m.

Do this by subtracting $\frac{2}{3}x$ from both sides of the equation:

$y = -\frac{2}{3}x + 12$

The slope of this line is $-\frac{2}{3}$ .

The slope of the perpendicular line is the negative reciprocal. Switch the numerator and denominator, and then multiply by :

$-\frac{2}{3} \Rightarrow -\frac{3}{2} \Rightarrow -\frac{3}{2} \times -1 \Rightarrow \frac{3}{2}$

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Example Question #5 : How To Find The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to $y=\frac{2}{3}x+\frac{1}{2}$ ?

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

$\frac{1}{3}$

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$-\frac{3}{2}$

Explanation:

In standard y=mx+b form, is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is $\frac{2}{3}$ . Therefore, the slope of the perpendicular line is $-\frac{3}{2}$ .

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Example Question #6 : How To Find The Slope Of A Perpendicular Line

Find the slope of this line: 2x-8y=16.

Possible Answers:

$m=-\frac{1}{4}$

m=-4

m=4

$m=\frac{1}{4}$

$m=\frac{3}{4}$

Correct answer:

$m=\frac{1}{4}$

Explanation:

Isolate for so that the equation now reads

$y=\frac{1}{4}x-2$

The slope is $\frac{1}{4}$ .

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High School Math : How to find the slope of a perpendicular line

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #2 : How To Find The Slope Of A Perpendicular Line

Example Question #4 : How To Find The Slope Of A Perpendicular Line

Example Question #3 : How To Find The Slope Of A Perpendicular Line

Example Question #2 : How To Find The Slope Of A Perpendicular Line

Example Question #4 : How To Find The Slope Of A Perpendicular Line

Example Question #5 : How To Find The Slope Of A Perpendicular Line

Example Question #6 : How To Find The Slope Of A Perpendicular Line

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